i 



;:*;. siKJt 




Class _^2^iZ 

Book i P^ f 

pe Copyri^htF 




mcrement 
increment 



^c 

I 



m(*rement 



CDPmiGHT DEPOSm 



Vol 



UniCS i^^ve been written on vch. 



j;iue ^mi 



'itten on 



quality and price 



BJItmore Timber Tables 




BY 

HOWARD R. KRINBILL 

COPYRIGHT. 1911 BY HOWARD R. KRINBILL 



FOR THE USE OF THE 

BILTMORE FOREST SCHOOL 
WORKING FIELDS, 1911-12: 

ADIRONDACKS, SOUTHERN APPALACHIANS, LAKE 
STATES. PACIFIC COAST AND GERMANY 



INTRODUCTION 63> W^v\ 

This booklet has been prepared for the use of the slu- 
dents of the Biltmore Forest School and may prove of 
interest to foresters and lumbermen in general. 

The original material consists of Compound Interest 
Keys for solving financial problems, Keys for the mental 
calculation of areas of circles, and Form Height Factors for 
estimating standing timber in board feet of lumber and in 
cords of wood and bark. 

The Mill Factor Method of estimating standing timber 
is employed by Dr. C. A. Schenck, who publishes a handy 
booklet of Cruiser's Tables giving contents in board feet for 
trees of any diameter, any number of logs up to 6, any taper 
per log from I inch to 4 inches, and any Mill Factor from 
5 to 8. 

The Volume Tables of "The Woodman's Handbook" have 
been used as a basis for working out Form Height Factors. 

The Tables for Use in Germany were compiled during 
an excursion through the forests of Germany. 

This booklet is the right size for inserting in ''The 
Woodman's Handbook" by Henry S. Graves, published by 
The United States Forest Service, or in "A Manual for 
Northern Woodsmen" by Austin Gary, published by Har- 
vard University. 



CCI.A2SSS63 



PROBLEMS IN FOREST FINANCE 
To Illustrate the, Utility of the Compound Interest !''eys 

1. The Report on the Standing Timber of the United 
States by Herbert Knox Smith, commissioner of corpora- 
tions, gives as examples of "enormous increase in value 
with great profits to the owners" during an interval of 40 
years: From $5 to $30 an acre, $7 to $40, $20 to $150, $1 to 
$18, $4 to $140, $1 to, $50. 

Question: What rate of interest do these "great 
profits" represent? 

2. Southern pine sold by the government 40 years ago 
at $1.25 per acre is now worth $60. Douglas Fir sold at 
$2.50 is now worth $100 to $200. What has been the annual 
price increment? 

3. If Yellow Poplar log run averaged $14 in 1895 and 
$30 in 1910, what has been the annual increase in stumpage 
value, assuming that the expense of production was $10? 

4 Timber worth $8 per acre in 1906 has increased 
yearly in volume 1 per cent, quality increment 2^ per cent, 
price increment 4 J per cent. Value in 1911? 

5. If stumpage prices increase 8 per cent, yearly, when 
will the investment double? When will investment increase 
threefold? Tenfold? 

6. In 1911 White Pine stumpage is worth $6 per M, 
Poplar $5, Oak $4, and Yellow Pine $3. What were the 
prices in 1890 and in 1900 if the annual price increment has 
been 10 per cent for White Pine, 8 per cent for Poplar and 
Oak, and 12 per cent, for Yellow Pine ? 



PROBLEMS 

7. In 1901, $1200 was paid for marked trees, equal 
volumes of White Pine, Poplar and Oak. The trees were to 
be cut in 5 years but in 1906 $700 was borrowed at 6 per 
cent, to pay for the privilege of letting the timber stand 
until 1911. How much was gained (or lost) by waiting until 
1911? The annual increments in volume, quality, and price 
were: White Pine, 3J per cent, 3 per cent, 8 per cent; 
Poplar 3 4-5, 2, 9; Oak 1 4-5, 1, 6. 

8. In 1900 a forest of 10,000 acres was bought for $70,- 

000. Taxes in 1900 were 6 cents per acre and advanced 
gradually to 15 cents in 1910. The lumber cut in 1900 was 
1000 M and increased steadily each year to 2000 M in 1910. 
Stumpage netted $2 per M in 1900 and rose steadily to $5 in 
1910. In 1904, a right of way was sold for $150; in 1905, a 
waterpower site brought $2500; in 1906, mineral rights, $3800; 
in 1907, tan bark $2750 net; in 1908, extract wood, $1320 net. 

In 1910, the property was sold for $20,000 cash, $10,000 
yearly for 5 years, and shares of U. S. Steel, some common 
at 77| and the rest preferred at 119. Question: How many 
shares of each were secured to make 7 per cent, on invest- 
ment, including taxes? 

ANSWERS 

1. $5 to $30= Aft- Value 6. Key 184. 184^40=-4.6 
per cent. (Case 3.) 

Similarly, the other rates of interest are 4.5 per 
cent, 5.2 per cent, 6.6, 9.1, and 10.1 per cent. 

2. $1.25 to $60=Aft- Value 48. Key 397. 1 
397^40=10 per cent. I 

$2.50 to $100= Aft- Value 40. Key i /p,,^ o\ 
378. 378^40=9i per cent. | ^^^^^ "^^ 

$2.50 to $200=Aft- Value 80, Key | 
449, 449-^40=11.2 per cent. I I 

3. $4 to $20= Aft- Value 5. Key 165. 165^15=11 
per cent. (Case 3.) 

4. 8 1-5 per cent. X 5 years=Key 41. Aft-Value 
1.5. 1.5X$8=$12. (Casel.) 

5. Aft-Value 2=Key 71. 71^8=9 years. (Case 4) 

6. Case 2. 7. Case 1. 8. Case 1, 5 and 6. 



COMPOUND INTEREST KEYS 

(Aft-Value is value at the end; Pre- Value is value at the beginning) 



Aft- 

VALUE 



1 
2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

25 

50 

100 

500 

1,000 

10,000] 

100,000 



TENTHS 



0.0 .1 0.2 0.3 0.4 0.5 0.6 0.7 0. 8 0.9 

KEYS (Number of Years x Rate of Interest) KEYS 



71 
113 
142 
165 

184 
199 
213 
225 
236 
246 
255 
262 
270 
278 
284 
288 
296 
301 
307 
330 
401 
472 
637 
708 
944 
1180 



10 


19 


27 


34 


41 


48 


54 


60 


76 


81 


85 


90 


94 


98 


102 


106 


116 


119 


122 


125 


128 


131 


134 


137 


145 


147 


150 


152 


154 


157 


159 


161 


167 


169 


171 


173 


175 


177 


179 


180 


186 


187 


189 


190 


192 


193 


195 


196 


200 


202 


203 


205 


206 


208 


209 


210 


214 


215 


217 


218 


219 


220 


221 


223 


226 


227 


228 


229 


231 


232 


233 


234 



66 
109 
140 
163 
182 
198 
211 
224 
235 



To obtain key of any omitted Aft-Value, add the 
keys of its factors. For example: 

Key of 29= Key of 10 plus Key of 2.9=345. 
Key of 36 =Key of 6 plus Key of 6 =368. 



Many problems may he solved 
mentally by remembering the 
Key for doubling, 71. 



How TO Use the Keys: 



Dase 


Given 


Wanted 


Solution 


1 
2 
3 
4 
5 

6 


per cent, and years 
per cent, and years 
Aft-Value and " 
per cent. & Af t-V. 
per cent, and years 

per cent, and years 


Aft-Value 

Pre-Value 

per cent. 

Years 

Aft-Value of 

$1 paid yearly 

Pre-Value of 

$1 paid yearly 


per cent, x years=Key to Aft-V. 
IH— Af t- Value= Pre-Value 
Key H— years =per cent. 
Key H— per cent.=years. 

Aft-Value of Key— 1 
per cent. 

Aft-Value of Key— 1 






per cent. X Aft- Value of Key 



MILL FACTORS 



The Mill Factor of a saw mill is its productive efficiency 
expressed in board feet of saw cut per cubic foot in the log. 
For example, Mill Factor 7 indicates that the mill produces 
7 and wastes 5 board feet for each cubic foot in the log. 

The unavoidable waste depends upon the following fac- 
tors: soundness of logs, taper of logs, diameter of logs, 
thickness of saw, thickness of boards, smallest width per- 
missible, quality ofmill machinery, skill of sawyer, inspection 
rules followed in edging and trimming, lowest marketable 
grade, and shrinkage. 

Under the most favorable conditions, in the case of 
straight, sound logs, a band mill will have a Mill Factor of 8, 
while a circular mill will generally be rated not higher than 7. 

The 40 or 50 different log rules used in the United States 
represent either constant or variable Mill Factors. Among 
the former are: 

The N. Hampshire or Blodgett Rule (115 Blodgett Feet per M) -Mill Factor 6. 
The Square of Two-thirds Rule ' " 6.8 

The Vermont Rule " " 7.6 

The Square of Three-fourths Rule " *' 8.6 

The most common log rules with variable Mill Factors 
are: 

It is evident that any given log rula 
is accurate for any given saw mill 
only where the Mill Factor of the 
log rule equals the Mill Factor of 
the saw mill. 

A standard method of log measure- 
ment would be to allow a certain 
number of board feet per cubic foot 
in the log. By comparing the solid 
cubic contents of a number of logs 
with the actual output in board feet 
of lumber, the Mill Factor of a mill 
is readily obtained. 

Page 8 shows the contents of 
sound trees in feet board measure 
by the Mill Factor Method. 





H w 


«.H 


a a 




J 3 


■^ ?5 J 


Z J 




(M 13 


ca w 3 


•-; j3 




s« 


^_S 


i^ 






= S 


BB 


.2- 


^^ 


i^ 


^U 


Q 


fe 


fe 


c^ 


6 


1.3 


6.1 


6.1 


9 


3.6 


5.7 


7.2 


12 


5.2 


6.3 


8.3 


15 


6.2 


7.3 


8.2 


18 


6.9 


7.4 


8.2 


21 


7.6 


7.9 


8.7 


24 


8.0 


8.0 


8.7 


30 


8.6 


8.4 


9.0 


36 


9 


8.2 


9.1 


40 


9.2 


8.6 


9.0 


50 


9.7 


8.6 




60 


10.0 


8.6 




120 


10.7 


8.8 





DOYLE BOARD FEET IN SOUND TREES 

(Taper above butt log=i to 3 inches) 



Diameter 


Taper and 


No. OF 


Fourteen Foot Logs 


Breast-High 


Bark of 










Outside Bark 


Butt Log 


1 


2 


3 


4 


12 


2.7 


25 


44 


53 


63 


15 


3.4 


51 


92 


117 


127 


18 


3.8 


92 


165 


217 


260 


21 


4 


146 


260 


357 


435 


24 


4.5 


211 


387 


541 


669 


27 


4.5 


297 


549 


773 


963 


30 


4.6 


400 


745 


1050 


1310 


33 


5 


506 


946 


1340 


1660 


36 


5.1 


630 


1190 


1660 


2060 


39 


5.6 


754 


1410 


1980 


2510 


42 


6.1 


890 


1670 


2350 


2970 


45 


6.6 


1030 


1950 


2740 


3470 


48 


7.1 


1190 


2250 


3170 


3990 


51 


7.7 


1350 


2550 


3620 


4540 


54 


8 


1540 


2890 


4080 


5080 


57 


8.8 


1710 


3220 


4540 


5650 


60 


9.2 


1920 


3560 


5010 


6250 



The lumberman wastes timber to save money; the con- 
sumer wishes him to waste money to save timber. 



CONTENTS OF SCUND TREES IN BOARD FEET 
MILL FACTOR 7 

(Taper above butt log=two inches per log) 



Small Diameter 

OF 


Number of Fourteen Foot Logs 


Butt Log 
Inside Bark 


1 


2 

39 
53 
69 


3 


4 


5 


6 


7 
8 
9 


26 

34 
43 


83 








10 
11 
12 


53 
65 

77 


88 
108 
130 


107 
134 
164 


147 
184 






13 
14 
15 


90 
105 
112 


155 

182 
210 


198 
235 
275 


224 
269 
318 


238 
288 
344 




16 

17 
18 


137 
154 
173 


241 
275 
310 


318 
365 
415 


372 

430 
492 


406 

473 
545 




19 
20 
21 


193 
214 
236 


347 

387 
428 


468 
524 
583 


558 
629 
703 


623 

706 
794 




22 

23 
• 24 


259 

283 
308 


472 
518 
566 


645 
711 

780 


782 
866 
953 


887 

986 

1090 




30- 
36 
42 


480 
686 
938 


896 
1309 
1792 


1260 
1855 
2569 


1568 
2338 
3262 


1827 
2758 
3878 




48 
54 
60 


1225 

1554 
1918 


2359 
3003 

3717 


3395 

4340 

5397 


4340 
5572 
6951 


5194 
6699 
8400 


5964 
7735 

9737 



KEYS FOR MENTAL CALCULATION OF AREA 
OF CIRCLES 



Diameter Class 


Base 


Key 


6 inches to 12 inches 


6 in 


ches = .2 sq. ft. 


.1 sq. ft. per in. 


12 " '' 24 *' 


12 


'' =.78 '' 


.2 " " " '* 


24 " '' 36 " 


24 


" =3.14 " 


.3 " " " " 


36 " "40^ " 


36 


- =7 


4 .. .. .. .. 


m " " 50 " 


m 


" =9 


.5 " '' '' ' 


50 '' " 60 " 


50 


'' =13.6 " 


.6 " '* '* '' 



The key to Square Feet Per Inch is the tens figure of 
the upper limit of the diameter class. 
How to use the Keys: 



Area 27 in. -=3.14+ (27 

Area38in.=7 -f (38— 36X.4) 



24X.3)=4.0sq. ft. 
~ 7.8 sq. ft. 



ESTIMATING STANDING TIMBER AT SIGHT 

After the Keys for Area of Circles are memorized, 
standing timber may be estimated at sight quickly and ac- 
curately by the Sectional Area— Form Height Factor Method 
af follows: 



No. OF 14 ft Logs 

(Taper above butt 
log equals 2 in. 
per log.) 



COTTENTS OF SOUND TREES IN BOARD FFET. 
MILL FACTOR 7 



Area of small end of butt log inside bark x 100 
Contents of a one log tree x If 

x3 
x3i 



The above method may be applied to any log rule having 
a constant Mill Factor by simply changing the length of log. 
For example: M. F. 8, log 12 ft. and M. F. 6, log 16 ft. 



FORM HEIGHT FACTORS 

Sedional Area Breast iiigliXf. H. f =[ords of 128 Cubic feel of Wood 













TOTAL HEIGHT IN 


FEET 






D tf 


t^ 


1 1 M 1 


1 






O W Q 


^ ^ M 


1 1 1 1 1 


I 




SPECIES 


Q Ph p:; 

hH O 


S ^ 3 
§ w ►^ 


405060708090100110120140 


160 




J H O 


< p^ ffi 


























O fe 


q" 




























6 


20 23 


28 


















Q 




9 


18 21 


25 


30 
















O 




12 


18 21 


23 


27 


31 














s i 




15 


17,20 22 


26 


29 


34 38 












18 


119 22 


25 


28 


321 36 










in vl 


90 


21 


|192l 


24 


27 


31 


34 










1 < 




24 




1821 


24 


27 


30 


33 












27 




18 


21 


24 


27 


30 


32 


34 








^ H 




30 






20 


23 


26 


29 


31 


33 








X 




36 








22 


25 


28 


31 


33 








W 




45 










26 


28! 30 


32 








Q 

o 




6 


2631 


36 


















£ o 




7 


2631 


37 


















° ^ S 

1 


80 


8 


27|32 38 


















down 


9 


33 38 


















to 1 inch 


10 




35 40 




















11 




37 43 


















w ^ m 

C/2 




12 




39 45 


















o^ 




6 


18 


22l28 


34 




















9 


20 


2630 


35 
















95 


12 




26|30 


34 
















"^ .. >y 


down 


15 






30 


33! 38 














SPR 

(For Fii 

Multip] 


to 4 in. 


18 






29 


32:36 


42 














21 








3213640 














24 








32S35 38 














27 








134^37 
















6 


22 


28 
























9 


22 


27 


33 




















12 




27 


32 


37 


43 


48 


53 












15 






31 


37 


42 


47 


52 


57 


63 






P-t 




18 








35140 


45 


50 


55 


60 






W 


90 


21 










38 


43 


48 


53 


57 










24 












42 


47 


52 


56 


66 




K 




27 












42 


46 


51 


56 


65 




^ 




30 
36 














46 
45 


50 
50 


55 
54 


64 
63 


72 






45 




















62 70 



SHORT-CUT FORM HEIGHT FACTORS 

S. A. Breast liighxf. H. f =Cords of 128 cubic feet of wood 



Species 



Cords of 128 Cu. Ft. 
Containing 



Total Height of 
Tree Feet 



F. H. F. 



Chesnut 



Second growth 
Hardwood 

Spruce 



Fir 



White Pine 



solid cubic feet 



(For Long Cords of 
160 cubic feet with 
112 solid cubic feet) 



solid down to 1 in. 



solid down to 4 in. 



95 solid down to 4 in. 



90 solid cubic feet 



75 ft. and under 
Over 75 ft. 

75 ft. and under 
Over 75 ft. 

30 ft. to 60 ft. 

65 ft. and under 
Over 65 ft. 

65 ft. and under 
Over 65 ft. 

80 ft. and under 
90 ft. to 100 ft. 

110 ft. to 120 ft. 
130 ft. to 170 ft. 



+ 10 

+ 11 

+ 8 
+ 9' 



-^ +D 



JH 

2 

3^H 

10 

ja 
2 

2 H 

5" 

H 

2 

_H^ 

2 

H 
2 

2JH 

5 



13 



- 2 

+ 2 

+ 2 



-2 



^ + 



SpJCOD 


s ^ 


T— 1 


§ 


JO aaquinu si^nBg 


1 1 


1 


1 


SHOXOV^ HHiawvia 


Qco^ 


Q 


Q 




^^o. 


<M 


CO 


HOiH xsvaaa 
aaxaiMviQ 


12-20 
21-33 


^l5Ss^^^g?S 


oo 


spaoo si^nba q3iq 


g 


■rj< CO(M 1-1 O Oi 


§ 


;sBajq -v -S x-^ "H A 








saioads 


>|B0 mm-) 


300^HaH 





HAY 



TABLES FOR USE IN GERMANY 



FORM HEIGHT FACTORS 

S. A. BreastHighXf. H. f.=Cordsof 128 
cubic feet with 90 of solid wood over 2 3-4 in. 



1 








pq 


1 








12; 


1 


o 




05 




6 


H 

m 


C/2 


tt, 


8 

C/2 




10 


18 


19 


14 




16 


21 


22 


20 


20 


21 


25 


26 


24 


25 


25 


28 


29 


26 


28 


28 


32 


32 


28 


32 


31 


34 


35 


31 


35 


35 


37 


38 


33 


38 


38 


40 


41 


35 


41 


41 


42 


43 


38 


44 


44 


45 


46 


40 


48 


47 


48 


48 


42 


51 


50 


50 


51 


45 


54 


53 


53 


53 


47 


58 


56 


54 


54 


50 


60 


58 


57 


57 


52 


63 




60 


59 


55 


68 




63 

+ 


60 

+ 








a| =^ 


K ^ 


a ^ 






.-V 


^^ 




1 


-"t 


4J 
<4H 






1 


W 


s 


g 




CD 


«D 


a; 
> 
o 
m 
0) 


> 

o 
tfi 
a> 

CD 

Eh 





S 



TO 



Q^ 



22 
25 

27 
30 
33 
35 
37 
39 
42 
43 
45 
47 
50 



(DO) 13 

0) ^ 



CO 

sL W2 "^ 



*- CO . 

•1- II o 3 -P -^ 

CD ;2S 



^Oi 



'O II X 



0) 0) 



offi 



Hi(M 



?H ?H "^ 

-Sol 



:::5 OS 
0) a; 



CO 



CD •• 

^ rn "^ 

0) 0) q; 



P- Sh ?-4 ^, CO C« 

,^ o) a; 5^^^ 



CO 



03 CO 



a c3 



a32gaS 



^ ~H3 "^ "o3 "^ "^ .S .S 

;3(73!=Si73:3^55m?h 






00 



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CD 

CO 0) 

-lJ 0) «+H 

if " 3 

I g II 

O "=*. HICO 

T-H C^^ LO 

CO O X 

^ X -^ 






0) 

S 
o 



q5 ^ 



^ c3 o 



Q ffi ^ CO ffi a 



The German Foresters 

Are. growing Oak in rotations of 150 years at 
$100 to $200 per thousand board feet, the Corner 
Stone of Conservative Forestry being High S'" 
age Price. 

The foundation for Destructive PVestry m 
aid by low prices and low tariff, high taxes an I 
high freight rates, /'hot iires and cold logic- 
free trade and unlimited competition. 



liiiifiii 



